Statistical properties of an iterated arithmetic mapping
type: Item
instance of: scholarly article
title: Statistical properties of an iterated arithmetic mapping
zbMATH Open document ID: 0845.11009
DOI: 10.1007/BF02188683
author: Yanyan Li
published in: Journal of Statistical Physics
publication date: 1994-01-01T00:00:00Z
review text: The ``Collatz''-problem (or ``\(3x+ 1\)''- or ``Hasse''- or ``Syracuse''- or ``Kakutani''-problem) is to prove that for every \(n\in \mathbb{N}\) there exists a \(k\) with \(T^{(k)}(n)= 1\), where the function \(T(n)\) takes odd numbers \(n\) to \((3n+ 1)/2\) and even numbers \(n\) to \(n/2\). This problem (and a similar trifurcation process) is studied from a probabilistic viewpoint, while the authors do not present any real new theoretical material. Through computer experiments it is shown that the occurring parities exhibit all properties of random sequences. It is a remarkable fact that even statistical physicists are interested in this elementary number theoretical problem.
reviewed by: Helmut Müller
Mathematics Subject Classification ID: 11B37
Mathematics Subject Classification ID: 11B83
Mathematics Subject Classification ID: 11K65
zbMATH DE Number: 843783
zbMATH Keywords: Collatz problem
zbMATH Keywords: trifurcation process
zbMATH Keywords: random sequences
MaRDI profile type: Publication
cites work: \(3x + 1\) search programs
cites work: Q4862542
cites work: Imitation of an Iteration
cites work: On the "3x + 1" Problem
cites work: The \(3x +1\) problem: Two stochastic models
cites work: The 3x + 1 Problem and Its Generalizations
cites work: A stopping time problem on the positive integers
cites work: Iteration of the number-theoretic function \(f(2n)=n\), \(f(2n+1)=3n+2\)
cites work: The set of rational cycles for the 3x+1 problem
full work available at URL: https://doi.org/10.1007/bf02188683
OpenAlex ID: W2093855919
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description: scientific article; zbMATH DE number 843783